A Handbook for Data Analysis in the Behavioral Sciences: Statistical Issues

By Gideon Keren; Charles Lewis | Go to book overview
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The Bayesian statement is a conditional one: Given something which is known, namely the data from our experiment, a degree of certainty is expressed about something which is unknown, namely the value of ψ. The sampling theory statement is also, according to a Bayesian at least, conditional, but the wrong conditioning is taking place. It is the unknown parameter value that is taken as given, rather than the known data. Indeed, as noted, the connection of the sampling theory statements to the data at hand is, at best, a tenuous one. It is not at all clear what one is supposed to think about a given computed interval from a sampling point of view. For the Bayesian, on the other hand, all attention is focused on the given interval, which refers directly to a posterior belief distribution. Results of future sampling or references to sampling distributions are irrelevant from this point of view.

To conclude, the difference between Bayesian and sampling theory statements may be stated even more sharply than before: Bayesian statements are directly relevant to the questions researchers ask. Sampling theory statements are not only indirect but of questionable relevance. Given this difference, the question posed earlier in this section may be rephrased. Why should anyone not switch from making sampling theory statements to making Bayesian ones?


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